Examples
As a simple geometric example, suppose it is desired to generate a random point within the unit circle. Generate a candidate point where and are independent uniformly distributed between −1 and 1. If it so happens that then the point is within the unit circle and should be accepted. If not then this point should be rejected and another candidate should be generated.
The ziggurat algorithm, a more advanced example, is used to efficiently generate normally-distributed pseudorandom numbers.
Read more about this topic: Rejection Sampling
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